Assumption 1 
For a compact set \(X \subset \mathbb {R}^n\) , let \(\kappa :\mathbb {R}^n\times \mathbb {R}^n\rightarrow \mathbb {R}\)  be a given kernel and \(\mathcal {H}_\kappa (X)\)  the reproducing kernel Hilbert space (RKHS) of functions over \(X\)  corresponding to \(\kappa \)  with norm \(\Vert  \cdot \Vert _\kappa \)  [1]}. Then, for each \(u \in U\)  and \(i\in \lbrace 1,...,n \rbrace ,\)  \(f^{(i)}(\cdot ,u) \in \mathcal {H}_\kappa (X)\)  and for a constant \(B_i>0,\)  it holds that \(\Vert  f^{(i)}(\cdot ,u) \Vert _\kappa \le B_i\) , where \(f^{(i)}\)  is the \(i\) -th component of \(f\) .

